The 35-year-old actress, her boyfriend Louis Dower, and her children Mia, 10, and Joe, 7, escaped along with 16 other guests from the eight-bedroom Great House on Necker Island, Branson's private island just north of Virgin Gorda in the British Virgin Islands.
Branson, who lost an office and thousands of pictures in the ruined building, was staying nearby with his wife and 25-year-old son Sam.
The incident occurred as then Tropical Storm Irene brushed past the Virgin Islands.
We had a really bad tropical storm with winds up to 90 miles per hour. A big lightning storm came around 4 a.m. and hit the house, Branson said Monday in a statement.
My son Sam rushed to the house and helped get everyone out.
Winslet's spokeswoman confirmed that the actress was unharmed.
Winslet reportedly carried Branson's 90-year-old mother Eve out of The Great House as the flames engulfed it.
She (Winslet) was staying there with her children and in fact it was she who carried my mother out of the house, Branson told Britain's ITV News.
She swept her up into her arms and got her out of the house as fast as possible, he added.
Branson also told ITV News that Winslet remarked it was like being in a film set where you're waiting for the words 'cut,' but they just don't come.
While the exact cause of the fire is under investigation, it is believed to have been caused by lightening.
We want to rebuild the house as soon as we can, Branson said in the statement. We have a wonderful staff here and we want them to stay in work. We'll all stay here for the time being. There's a lot of damage and we won't be able to stick it back together again right away. It was a beautiful house.
Branson bought Necker Island in the early 1980s. The island can be hired privately for $54,500 a night.